Having recently joined this game, I am greatly enjoying it, except for some very major issues in the UI. These are very basic things that greatly frustrate me, and impede my enjoyment of the game. They are also very basic usability and UI design issues. Here are the most major offenders:

The Repair Screen (Injury UI): Why does this clunky, over-designed piece of junk even exist? Double clicking the relevant regen/component should just remove one injury debuff from you, done. Having to open a menu, select the injury, the number of injuries, click okay, repeat, then close the menu is several steps too many. Simplicity!

The Mail Screen: Mostly simple, standard and functional except for one thing: The dropdown suggesting characters when I have input a @handle needs to time out, or disappear on clicking something else. Currently, it blocks the subject field except for a small area of pixels at the bottom left. It can be gotten around by entering subject first, but it's still a very basic piece of UI design that should be implemented.

Non stacking conversation windows: Some windows are considered 'conversations' when they really don't need to be. This is most noticable in the duty officer interface, department head recommendations. Opening the Replicator to get commodities closes the department. Why? It doesn't need to, and for someone like me who tends to forget whether they needed 2 Self Sealing Stem Bolts or 3, it just means more circular clicking.

Mudd Trader! Related to the above, it is EXTREMELY annoying to have this guy pop up in Sirius Sector when I'm trying to buy commodities from another trader or fill out doff missions. I wasn't talking to him, I don't want his wares, quite honestly, I want to blow his ship into tiny little bits of space debris for bothering me. His 'closing up shop' trigger should ONLY be given to those who were actually conversing with him.

Inconsistency of Menu Availability: Beam down to Starfleet Academy from anywhere, but I have to get close to dock with Earthspace Dock. Ditto for Qo'nos. I can beam out from SFA / KA to anywhere, but everywhere else uses the normal Beam Out button by the minimap, except the Fleet Starbase where I can only beam out on the transporter pad. Pick one design and stick to it, please.

Inconsistency of NPC interaction range: If I walk up to the personal officer in Starfleet Academy, it's because I want to talk to her, not Lt Fera behind her. Many times I've run up and hit F and gotten the wrong NPC. Same for the datachip dispensing library computer. I'm sure there are other examples out there. Please adjust the interaction range for these NPCs to be consistent.

UI Options that should be On by default, aren't: Keep Moving During Contact Dialogues is one of them - I got killed many times by being unable to move thanks to a conversation popping up until another player told me I could change it. Spaceship weapon autofire should also be on by default. This isn't Diablo, I don't need to spam click to fire.

More documentation of options: Related to the above: I didn't know about gun autofire until about 4 days after I started playing, when I found it by accidentally right clicking. I didn't know about the contact dialogue thing at all til another player told me. Some of these things really could stand to have better help text referencing them.

More major issue: Red on orange on yellow on red: Yeap, the KDF UI in general. It's horrible, to be honest. It gives me eye strain, and I can't play KDF for more than a couple of hours. Anecdotal, but I hear a lot of players in game with similar complaints. Many games offer the ability to customise UI colours, or go for neutral tones like grays, browns and soft golds. I accept that Red is lore based, and proper for a KDF ship, but for the sake of playability the option should be there to change it. A simple "Use Federation Colour Scheme" in the options menu would be all it takes.

These are mostly little things, but they are very basic elements of usability and user-friendliness. They add up to a very frustrating experience with the game some times. I really enjoy it, since it's one of the better space combat MMo - space combat games in general really - out at the moment. But it could be so much better if these little things were fixed.

I have to say, I agree with pretty much EVERYTHING on that list. Quality-of-Life improvements is something this game could sorely need. Some improvements are being made to the Quest Tracker area, but as you pointed out, the most egregious issues with the game, stems from the various UI issues/windows.

I'd like to see the next Ask Cryptic to have a question asking for comprehensive quality-of-life improvements.

Expanded upon your "map travel" suggestion, as well as provided a few examples of how it currently is ingame, and how it could behave in the future. I'll attempt to update my topic later today (hopefully after some additional comments have been made).

100% agreement here too.
For all the good it will do, players have been complaining about the Klingon UI and sometimes the Federation one for a long time and so far other than vague comments in devblogs about how they are investigating it, nothing.
A comprehensive players guide for game configuration is sadly needed, it's possible to search the forums or ask questions there, some good people can and do offer help, but it still involves looking through a maze of random comments, outright insults and useless trivia to find useful information. There is the Star Trek wiki but no one yet has taken the time to compile a user guide for game configuration there.
The game incorporates no UI modification ability, otherwise there are many enterprising users that would have by now designed UIs far superior to any of Cryptic's offerings.
UI mod support is something Cryptic should seriously consider, it would allow users to create UIs to their own tastes whilst relieving Cryptic of the time and effort of designing UIs that may or may not suit everyone's desires. The added benefits of allowing users to make a direct useful contribution to the game should be self evident.

I'm glad to see people agree with me. It's not that I don't enjoy the game (Well, except playing kdf), but that I would enjoy it a lot more if these little things were solved. A little polish would go a LONG way to improving the overall quality of STO.